Geometric realizations of generalized algebraic curvature operators
arXiv:0811.3180 · doi:10.1063/1.3049619
Abstract
We study the 8 natural GL equivariant geometric realization questions for the space of generalized algebraic curvature tensors. All but one of them is solvable; a non-zero projectively flat Ricci antisymmetric generalized algebraic curvature is not geometrically realizable by a projectively flat Ricci antisymmetric torsion free connection.